Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916217882673152 |
|---|---|
| author | Balci, Anna Kh. Kaltenbach, Alex |
| author_facet | Balci, Anna Kh. Kaltenbach, Alex |
| contents | In the present paper, we examine a Crouzeix-Raviart approximation of the $p(\cdot)$-Dirichlet problem. We derive a $\textit{medius}$ error estimate, $\textit{i.e.}$, a best-approximation result, which holds for uniformly continuous exponents and implies $\textit{a priori}$ error estimates, which apply for Hölder continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10687 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem Balci, Anna Kh. Kaltenbach, Alex Numerical Analysis 49M29, 65N15, 65N30, 35J60, 46E30 In the present paper, we examine a Crouzeix-Raviart approximation of the $p(\cdot)$-Dirichlet problem. We derive a $\textit{medius}$ error estimate, $\textit{i.e.}$, a best-approximation result, which holds for uniformly continuous exponents and implies $\textit{a priori}$ error estimates, which apply for Hölder continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings. |
| title | Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem |
| topic | Numerical Analysis 49M29, 65N15, 65N30, 35J60, 46E30 |
| url | https://arxiv.org/abs/2303.10687 |